Answer
$T_1 = 4.55~N$
Work Step by Step
In part (a), we found that $a = 1.57~m/s^2$
We can consider the forces on $m_1$ to find $T_1$:
$T_1 - m_1~g = m_1~a$
$T_1 = m_1~(g+a)$
$T_1 = (0.400~kg)~(9.8~m/s^2+1.57~m/s^2)$
$T_1 = 4.55~N$
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